Metamaterials--artificially structured materials with tailored electromagnetic response--can be designed to have properties difficult to achieve with existing materials. Here we present a structured metamaterial, based on conducting split ring resonators (SRRs), which has an effective index-of-refraction with a constant spatial gradient. We experimentally confirm the gradient by measuring the deflection of a microwave beam by a planar slab of the composite metamaterial over a broad range of frequencies. The gradient index metamaterial represents an alternative approach to the development of gradient index lenses and similar optics that may be advantageous, especially at higher frequencies. In particular, the gradient index material we propose may be suited for terahertz applications, where the magnetic resonant response of SRRs has recently been demonstrated.
We further miniaturize a recently established silver-based negative-index metamaterial design. By comparing transmittance, reflectance and phase-sensitive time-of-flight experiments to theory, we infer a real part of the refractive index of -0.6 at 780 nm wavelength -- which is visible in the laboratory.
In this paper, we numerically demonstrate a near-infrared negative-index metamaterial (NIM) slab consisting of multiple layers of perforated metal-dielectric stacks and exhibiting low imaginary part of index over the wavelength of negative refraction. The effective index is obtained using two different numerical methods and found to be consistent. Backward phase propagation is verified by calculation of fields inside the metamaterial. These results point to a new design of low loss thick metamaterial at optical frequencies.
We demonstrate experimentally and numerically that nonplanar chiral metamaterials give giant optical activity, circular dichroism, and negative refractive index. The transmission, reflection, and the retrieval results of the experiments agree pretty well with the simulations. This is an important step toward the design and fabrication of three-dimensional isotropic chiral metamaterials.
Metamaterials offer unprecedented flexibility for manipulating the optical properties of matter, including the ability to access negative index, ultra-high index and chiral optical properties. Recently, metamaterials with near-zero refractive index have drawn much attention. Light inside such materials experiences no spatial phase change and extremely large phase velocity, properties that can be applied for realizing directional emission, tunneling waveguides, large area single mode devices, and electromagnetic cloaks. However, at optical frequencies previously demonstrated zero- or negative-r…
We propose a design for a plasmonic copper metamaterial with a negative index of refraction at visible/near-infrared wavelengths. Using numerical simulations, we demonstrate negative refraction by a copper metamaterial prism, and perform a parameter extraction technique to verify the sign of the effective, electric permittivity and magnetic permeability. Our proposed design has a figure of merit comparable to similar silver-based metamaterials operating in the visible/near-infrared range. These findings have implications for the design of low cost plasmonic devices and negative-index metamater…
We show the designs of one- and two-dimensional photonic negative index metamaterials around telecom wavelengths. Designed bulk structures are inherently connected, which render their fabrication feasible by direct laser writing and chemical vapor deposition.
We propose a design for broadband waveguide mode conversion based on gradient index metamaterials (GIMs). Numerical simulations demonstrate that the zeroth order of transverse magnetic mode or the first order of transverse electric mode (TM0/TE1) can be converted into the first order of transverse magnetic mode or the second order of transverse electric mode (TM1/TE2) for a broadband of frequencies. As an application, an asymmetric propagation is achieved by integrating zero index metamaterials inside the GIM waveguide.
The paper considers an opportunity for the creation of an artificial two-component metamaterial with a negative refractive index within the radio and optical frequency band, which possesses a spatial dispersion. It is shown that there exists a spectral region where, under certain ratio of volume fraction unit occupied with components, the metamaterial appears transparent without attenuating the electromagnetic wave passing through it and possessing a phase and group velocity of the opposite sign.
We discuss optical constants in artificial metamaterials showing negative magnetic permeability and electric permittivity. Using effective field theory, we calculate effective permeability of nanofabricated media composed of pairs of identical gold nano-pillars with magnetic response in the visible spectrum.
We present the blueprint for a novel negative-index metamaterial. This structure is fabricated via three-dimensional two-photon direct laser writing and silver shadow evaporation. The comparison of measured linear optical spectra with theory shows good agreement and reveals a negative real part of the refractive index at around 3.85 micrometer wavelength - despite the fact that the metamaterial structure is bi-anisotropic due to the lack of inversion symmetry along its surface normal.
A robust wedge setup is proposed to unambiguously demonstrate negative refraction for negative index metamaterials. We applied our setup to several optical metamaterials from the literature and distinctly observed the phenomena of negative refraction. This further consolidates the reported negative-index property. It is found there generally exists a lateral shift for the outgoing beam through the wedge. We derived a simple expression for calculating this beam shift and interestingly, it provides us a strategy to quantitatively estimate the loss of the wedge material (Im[n]). Addition- ally, w…
We theoretically investigate the possibility of using a metamaterial structure as a spacer, named as metaspacer, which can be integrated with other materials in microfabrication. We show that such metaspacers can provide new optical behaviors that are not possible through conventional spacers. In particular, we investigate negative index metaspacers embedded in fishnet metamaterial structures and compare them with conventional fishnet metamaterial structures. We show that the negative index metaspacer based fishnet structure exhibits intriguing inverted optical response. We also observe that t…
A type of 3-dimensional optical negative-refractive-index metamaterials composed of all dielectric nanospheres is proposed and demonstrated theoretically. The metamaterials are constructeded by pairing together two kinds of dielectric nanospheres as concentric shells embedded in a host medium. Mie-based extended effective theory shows that the dielectric core and the dielectric shell provide the negative permeability and the negative permittivity, respectively, both due to the strong Mie resonances. Within the coupled resonant frequency region, the negative index of refraction can be achieved.
We demonstrate a metamaterial that cannot be described by a single set of refractive-index and impedance values, even for fixed frequency and polarization. The metamaterial structure is a stack of dissimilar waveguides with subwavelength width and spacing, which guide light at different phase velocities. This multi-refractive-index metamaterial (MRIM) can be viewed as a spatial superposition of multiple homogeneous materials. Using full-wave simulations, we demonstrate several optical components based on MRIMs, including prisms that deflect light to multiple angles, lenses with multiple focal …
We propose and investigate a new type of metamaterial structure composing of several interpenetrating wire meshes. Calculated band structures show that they exhibit index ellipsoids locating at nonzero k-point in long wavelength limit. We can comprehend these quasistatic modes by Poison's equation and find these modes do not rely on the detailed geometry of the wires but the connectivities of the wires. We can engineer the locations of index ellipsoid by designing the connectivities of the wire meshes.
A well-established, silver fishnet design has been further miniaturized to function as a negative-index material at the shortest wavelength to date. By studying the transmittance, reflectance, and corresponding numerical simulations of the sample, we report in this paper a negative refractive index of -0.25 at the yellow-light wavelength of 580 nm.
An electric inductor-capacitor (ELC) resonator provides a series of electrical resonances and a pair of ELC resonators leads to the split of each resonance into two modes, i.e., magnetic and electric modes, corresponding to antisymmetric and symmetric current distributions. With the meticulous design of the ELC resonator, we can achieve a negative index metamaterial through mode hybridization by overlapping the first electric resonance mode and the second magnetic resonance mode. Such non-connected designs may offer opportunities to achieve three-dimensional negative index metamaterials.
We present simulation results of a design for negative index materials that uses magnetic resonators to provide negative permeability and metal film for negative permittivity. We also discuss the possibility of using semicontinuous metal films to achieve better manufacturability and enhanced impedance matching.
An effective medium model is developed for disordered metamaterials containing a spatially random distribution of dielectric spheres. Similar to effective medium models for ordered metamaterials, this model predicts resonances in the effective permeability and permittivity arising from electric- and magnetic-dipole Mie resonances in the spheres. In addition, the model predicts a redshift of the electric resonance with increasing particle loading. Interestingly, when the particle loading exceeds the percolation threshold of 33\%, the model predicts that the electric resonance overlaps with the …
We demonstrated a 2D helical chiral metamaterial that exhibits broadband strong optical activity resulting nonresonant Drude-like response. The strong chirality leads to broadband negative refractive index with high figure of merit (>90) and extremely low loss (<2% per layer). The optical activity are insensitive to the angles of incident electromagnetic waves, thereby enabling more flexibility in polarization manipulation applicaitons.
A metamaterials-based approach to making a wide-angle absorber of infrared radiation is described. The technique is based on an anisotropic Perfectly Impedance Matched Negative Index Material (PIMNIM). It is shown analytically that a sub-wavelength in all three dimensions PIMNIM enables absorption of close to 100% for incidence angles up to $45°$ to the normal. A specific implementation of such frequency-tunable PIMNIM based on plasmonic metamaterials is presented. Applications to infrared imaging and coherent thermal sources are described.
Zero-index materials exhibit exotic optical properties that can be utilized for integrated-optics applications. However, practical implementation requires compatibility with complementary metallic-oxide-semiconductor (CMOS) technologies. We demonstrate a CMOS-compatible zero-index metamaterial consisting of a square array of air holes in a 220-nm-thick silicon-on-insulator (SOI) wafer. This design is achieved through a Dirac-cone dispersion. The metamaterial is entirely composed of silicon and offers compatibility through low-aspect-ratio structures that can be simply fabricated in a standard …
Nonlinear metamaterials (NLMMs) have been predicted to support new and exciting domains in the manipulation of light, including novel phase matching schemes for wave mixing. Most notable is the so-called nonlinear-optical mirror, in which a nonlinear negative-index medium emits the generated frequency towards the source of the pump. For the first time, we experimentally demonstrate the nonlinear-optical mirror effect in a bulk negative-index NLMM, along with two other novel phase matching configurations, utilizing periodic poling to switch between the three phase matching domains.
We theoretically study fishnet metamaterials at optical frequencies. In contrast to earlier works, we provide a microscopic description by tracking the transversal and longitudinal flows of energy through the fishnet mesh composed of intersecting subwavelength plasmonic waveguides. The analysis is supported by a semi-analytical model based on surface-plasmon coupled-mode equations, which provides accurate formulas for the fishnet refractive index, including the real-negative and imaginary parts. The model simply explains how the surface plasmons couple at the waveguide intersections and it shi…
The race to engineering metamaterials comprising of a negative refractive index in the optical range has been fueled by the realization of negative index materials for GHz frequencies six years ago. Sheer miniaturization of the GHz resonant structures is one approach. Alternative designs make use of localized plasmon resonant metal nanoparticles or nanoholes in metal films. Following this approach, a negative refractive index has been realized in the optical range very recently. We review these recent results and summarize how to unambiguously retrieve the effective refractive index of thin la…
We present a gradient-index (GRIN) metamaterial based on an array of annular slots. The structure allows a large variation of the effective refractive index under normal-to-plane incidence and thus enables the construction of GRIN devices consisting of only a small number of functional layers. Using full-wave simulations, we demonstrate the annular slot concept by means of a 3-unit-cell thin GRIN lens for the terahertz (THz) range. In the presented realizations, we achieved an index contrast of Delta n = 1.5 resulting in a highly refractive lens suitable for focusing THz radiation to a spot si…
Negative index metamaterials (NIMs) give rise to unusual and intriguing properties and phenomena, which may lead to important applications such as superlens, subwavelength cavity and slow light devices. However, the negative refractive index in metamaterials normally requires a stringent condition of simultaneously negative permittivity and negative permeability. A new class of negative index metamaterials - chiral NIMs, have been recently proposed. In contrast to the conventional NIMs, chiral NIMs do not require the above condition, thus presenting a very robust route toward negative refracti…
Isotropic negative index metamaterials (NIMs) are highly desired, particularly for the realization of ultra-high resolution lenses. However, existing isotropic NIMs function only two-dimensionally and cannot be miniaturized beyond microwaves. Direct laser writing processes can be a paradigm shift toward the fabrication of three-dimensionally (3D) isotropic bulk optical metamaterials, but only at the expense of an additional design constraint, namely connectivity. Here, we demonstrate with a proof of-principle design that the requirement connectivity does not preclude fully isotropic left-hande…
The recent advance in the assembly of metallic nanoparticles (NPs) has enabled sophisticated engineering of unprecedented light-matter interaction at the optical domain. In this work, I expand the design flexibility of NP optical metamaterial to push the upper limit of accessible refractive index to the unnaturally high regime. The precise control over the geometrical parameters of NP superlattice monolayer conferred the dramatic increase in electric resonance and related effective permittivity far beyond the naturally accessible regime. Simultaneously, effective permeability, another key fact…
One of the most fundamental properties of isotropic negative-index metamaterials, namely opposite directionality of the Poynting vector and the wavevector, enable many novel linear and nonlinear regimes of light-matter interactions. Here, we predict distinct characteristics of azimuthal modulation instability of optical vortices with different topological charges in negative-index metamaterials with Kerr-type and saturable nonlinearity. We derive an analytical expression for the spatial modulation-instability gain for the Kerr-nonlinearity case and show that a specific condition relating the d…
To study the scattering properties of metamaterials, we generalize two scattering methods developed for conventional (non-magnetic) isotropic materials to the case of materials with arbitrary values (positive or negative) of magnetic permeability and electric permittivity. The generalized methods are used to study the changes in the reflectivity of a metamaterial surface with localized roughness when the relative refractive index changes sign. Our results show that, unlike the case of a plane surface whose reflectivity is unaffected by the change of sign of the relative refractive index, in ro…
The extraordinary properties of nonlinear optical propagation processes in double-domain positive/negative index metamaterials are reviewed. These processes include second harmonic generation, three- and four-wave frequency mixing, and optical parametric amplification. Striking contrasts with the properties of the counterparts in ordinary materials are shown. We also discuss the possibilities for compensating strong losses inherent to plasmonic metamaterials, which present a major obstacle in numerous exciting applications, and the possibilities for creation of unique ultracompact photonic dev…
We realize variable control of the group delay in an electromagnetically induced transparency-like metamaterial. Its unit cell is designed to have a bright mode and a dark mode. The coupling strength between these two modes is determined by the electromagnetic field gradient. In this metamaterial with field-gradient-induced transparency, the group delay at the transparency frequency can be varied by varying the incident angle of the electromagnetic plane waves. By tilting a single layer of the metamaterial, the group delay of a microwave pulse can be varied between 0.50 and 1.85 ns.
We theoretically and numerically investigate the phenomenon of resonant field enhancement of Gaussian beams in two types of transition metamaterials: with a positive-zero-negative index profile and with a positive-zero-positive index profile and demonstrate strongly localized resonant field enhancement in both cases. This study is likely to have applications in the fields of nano-optics, sub-wavelength imaging, and nano-fabrication and lays a foundation for the studies of more complex vector and vortex beam propagation in graded-index metamaterials.
High-index dielectric materials are in great demand for nanophotonic devices and applications, from ultrathin optical elements to metal-free sub-diffraction light confinement and waveguiding. Here we show that chalcogenide topological insulators are particularly apt candidates for dielectric nanophotonic architectures in the infrared spectral range by reporting metamaterial resonances in chalcogenide crystals sustained well inside the mid-infrared, choosing Bi$_2$Te$_3$ as case study within this family of materials. Strong resonant modulation of the incident electromagnetic field is achieved t…
We investigate a dynamically controllable electromagnetically induced transparency-like metamaterial. The unit structure of the metamaterial consists of a low-quality-factor resonator and a high-quality-factor resonator. The field gradient of the incident electromagnetic wave in the transverse direction induces coupling between these two types of resonators and causes a transparency phenomenon. We present the simulation and experimental results for the dynamic control of the electromagnetic response.
We demonstrate that surface plasmons of a thin metal film interacting with a periodic array of nano-structures around it can be utilized to make bulk negative index metamaterials at visible spectrum with simultaneously negative permittivity and permeability. These surface plasmon driven metamaterials have high figure of merit and can be tuned arbitrarily to operate at any wavelength in the visible spectrum and possibly at ultraviolet spectrum. We numerically demonstrate the idea by a metamaterial structure which exhibits a strong magnetic response resulting in a negative index of refraction in…
We show experimentally the successful use of colloidal lithography for the fabrication of negative index metamaterials in the near-infrared wavelength range. In particular, we investigated a specific implementation of the widely studied double fishnet metamaterials, consisting of a gold-silica-gold layer stack perforated by a hexagonal array of round holes. Tuning of the hole diameter allows us to tailor these self-assembled metamaterials both as single- (ε < 0) and double (ε < 0 and μ < 0) negative metamaterials.
We study experimentally the dynamic tunability and self-induced nonlinearity of split-ring resonators incorporating variable capacitance diodes. We demonstrate that the eigenfrequencies of the resonators can be tuned over a wide frequency range, and significantly, we show that the self-induced nonlinear effects observed in the varactor-loaded split-ring resonator structures can appear at relatively low power levels.
We develop a concept for a waveguide that exploits spatial control of nonlinear surface-polaritonic waves. Our scheme includes an optical cavity with four-level $\text{N}$-type atoms in a lossless dielectric placed above a negative-index metamaterial layer. We propose exciting a polaritonic Akhmediev breather at a certain position of the interface between the atomic medium and the metamaterial by modifying laser-field intensities and detunings. Furthermore, we propose generating position-dependent polaritonic frequency combs by engineering widths of the electromagnetically induced transparency…
Plasmonic metamaterials support the localized surface plasmon resonance (LSPR), which is sensitive to the change in the dielectric environment and highly desirable for ultrasensitive biochemical sensing. In this work, a novel design of supercell metamaterials of four mutually rotating split ring resonators (SRRs) is proposed, where simultaneous excitations of odd (N=1 and N = 3) and even (N=2) resonance modes are realized due to additional asymmetry from the rotation and show insensitivity to two orthogonal polarizations. The full utilization of these three resonance dips show bright prospects…
We investigate the magnetic response of meta-atoms that can be fabricated by a bottom-up technique. Usually such meta-atoms consist of a dielectric core surrounded by a large number of solid metallic nanoparticles. In contrast to those meta-atoms considered thus far, we study here for the first time hollow metallic nanoparticles (shells). In doing so we solve one of the most pertinent problems of current self-assembled metamaterials, namely implementing meta-atoms with sufficiently large resonance strength and small absorption. Both conditions have to be met for deep sub-wavelength meta-atoms …
We designed and implemented a gradient index metasurface for the in-plane focusing of confined terahertz surface waves. We measured the spatial propagation of the surface waves by two-dimensional mapping of the complex electric field using a terahertz near-field spectroscope. The surface waves were focused to a diameter of 500 \micro m after a focal length of approx. 2 mm. In the focus, we measured a field amplitude enhancement of a factor of 3.
This work is concerned with the experimental demonstration of a dual-band negative index metamaterial. The sample is double-negative (showing both a negative effective permeability and a negative effective permittivity) for wavelengths between 799 and 818 nm of linearly polarized light with a real part of refractive index of about -1.0 at 813 nm; the ratio -Re(n)/Im(n) is close to 1.3 at that wavelength. For an orthogonal polarization, the same sample also exhibits a negative refractive index in the visible (at 772 nm). The spectroscopic measurements of the material are in good agreement with …
Metamaterials have introduced a whole new world of unusual materials with functionalities that cannot be attained in naturally occurring material systems by mimicking and controlling the natural phenomena at subwavelength scales. However, the inherent absorption losses pose fundamental challenge to the most fascinating applications of metamaterials. Based on a novel plasmon injection (PI or Π) scheme, we propose a coherent optical amplification technique to compensate losses in metamaterials. Although the proof of concept device here operates under normal incidence only, our proposed scheme ca…
We investigate a class of multilayered metamaterials characterized by moderate-index inclusions and low average permittivity. Via first-principle calculations, we show that in such scenario first- and second-order spatial dispersion effects may exhibit a dramatic and non-resonant enhancement, and may become comparable to the local response. Their interplay gives access to a wealth of dispersion regimes encompassing additional extraordinary waves and topological phase transitions. In particular, we identify a novel configuration featuring bound and disconnected isofrequency contours. Since they…
The extraordinary properties of laser-induced transparency of a negative-index slab and parametric amplification for a backward-wave signal are investigated. The effects of the idler absorption and phase mismatch on the amplification of the signal are studied, and the feasibility of ensuring robust transparency for a broad range of control field intensities and slab thicknesses is shown. A particular option consisting of the independent engineering of a strong four-wave mixing response and the negative refractive index is proposed and its specific features are investigated. The feasibility of …
Extreme mid-infrared field enhancement and anapoles in high-index plasmonic metamaterials
School of Physics and Astronomy, University of Birmingham（伯明翰大学物理与天文学学院）；NanoPhotonics Centre, Cavendish Laboratory, University of Cambridge（剑桥大学卡文迪许实验室纳米光子学中心）
e present a detailed study of the retrieved optical parameters, electrical permittivity, magnetic permeability and refractive index, of the coupled fishnet metamaterial structures as a function of the separation between layers. For the weak coupling case, the retrieved parameters are very close to the one-functional-layer results and converge relatively fast. For the strong coupling case, the retrieved parameters are completely different than the one unit fishnet results. We also demonstrate that the high value of the figure of merit (FOM=|Re(n)/Im(n)|) for the strongly coupled structures is d…
We report the experimental demonstration of broadband negative refractive index obtained in a labyrinthine acoustic metamaterial structure. Two different approaches were employed to prove the metamaterial negative index nature: one-dimensional extractions of effective parameters from reflection and transmission measurements, and two-dimensional prism-based measurements that convincingly show the transmission angle corresponding to negative refraction. The transmission angles observed in the latter case also agree very well with the refractive index obtained in the one-dimensional measurements …
A key optical parameter characterizing the existence of negative refraction in a thin layer of a composite material is the effective refractive index of an equivalent, homogenized layer with the same physical thickness as the initial inhomogeneous composite. Measuring the complex transmission and reflection coefficients is one of the most rigorous ways to obtain this parameter. We dispute Grigorenko's statement (Optics Letters 31, 2483 (2006)) that measuring only the reflection intensity spectrum is sufficient for determining the effective refractive index. We discuss fundamental drawbacks of …
An array of pairs of parallel gold nanorods is shown to have a negative refractive index n'=-0.3 at the optical communication wavelength of 1.5 micron. This effect results from the plasmon resonance in the pairs of nanorods for both the electric and magnetic components of light. The refractive index is retrieved from the direct phase and amplitude measurements for transmission and reflection, which are all in excellent agreement with our finite difference time domain simulations. The refraction critically depends on the phase of the transmitted wave, which emphasizes the importance of phase me…
Zero-index metamaterials (ZIMs) offer unprecedented ways to manipulate the flow of light, and are of interest for wide range of applications including optical cloaking, super-coupling, and unconventional phase-matching properties in nonlinear optics. Impedance-matched ZIMs can be obtained through a photonic Dirac-cone (PDC) dispersion induced by an accidental degeneracy of two linear bands - typically an electric monopole mode and a transverse magnetic dipole mode - at the center of the Brillouin zone. Consequently, PDC can only be achieved for a particular combination of geometric parameters …
We study the propagation of light in a three-dimensional double-periodic Ag/TiO2 multilayer metamaterial composed of coupled plasmonic waveguides operating in the visible and UV spectral range. For these frequencies, light propagation in the plane of the waveguides is described by a negative phase velocity, while for the orthogonal direction light propagation is described by a Bloch wave composed of a large number of harmonics. As a result, the material cannot generally be described by a single phase index: decomposing the Bloch wave into different harmonics we show that for the wavelength ran…
A novel active negative index metamaterial that derives its gain from an electron beam is intro- duced. The metamaterial consists of a stack of equidistant parallel metal plates perforated by a periodic array of holes shaped as complementary split-ring resonators. It is shown that this structure supports a negative-index transverse magnetic electromagnetic mode that can resonantly interact with a relativistic electron beam. Such metamaterial can be used as a coherent radiation source or a particle accelerator.
Optically isotropic metamaterials (MMs) are required for the implementation of subwavelength imaging systems. At first glance one would expect that their design should be based on unit cells exhibiting a cubic symmetry being the highest crystal symmetry. It is anticipated that this is a sufficient condition since it is usually assumed that light does not resolve the spatial details of MM but experiences the properties of an effective medium, which is then optically isotropic. In this work we challenge this assumption by analyzing the isofrequency surfaces of the dispersion relation of the spli…
We present the vertically illuminated Si compatible mid-infrared photodetectors based on graphene that forms negative-index metamaterial. The coupling into a 2D layer at the angles near normal to the surface is negligible without the help of a metamaterial. We propose a low loss metamaterial, the dielectric structure with the nano/microholes through 2D materials that supports a resonance and enhances quantum efficiency in a wide range of incident angles.
The authors introduce a general mechanism, based on electrostatic and magnetostatic considerations, for designing three-dimensional isotopic metamaterials that possess an enhanced refractive index over an extremely large frequency range. The mechanism allows nearly independent control of effective electric permittivity and magnetic permeability without the use of resonant elements.
